A numeral system in a way to represent or express numbers using digits or other symbols in a consistent manner.
The most widely used numeral system by people is decimal, or BASE 10.
Definitions
10^4
In the example above, the number 10 is called the BASE (or radix / root), and the number 4 is called the exponent. The exponent corresponds to the number of times the base is used as a factor (4 x 4 x 4 x 4).
Binary (0, 1) - used by logic gates in most digital circuits
To convert the binary number 1011 to decimal,
1 0 1 1 # Your binary number
(1x2^3) + (0x2^2) + (1x2^1) + (1x2^0) # Multiply your number by the power of the base that the digit represents
8 + 0 + 2 + 1 = 11 # Add the numbers together to get the result in BASE 10
Octal (0..7) - used often in computing
To convert the octal number 350 into decimal,
3 5 0 # Your octal number
(3x8^2) + (5x8^1) + (0x8^0) # Multiply your number by the power of the base that the digit represents
192 + 40 + 0 = 232 # Add the numbers together to get the result in BASE 10
Hexadecimal, hex (0..9, a..f) - used often in computing
To convert the hex number 1F20 into decimal,
1 F 2 0 # Your hex number
(1x16^3) + (Fx16^2) + (2x16^1) + (0x16^0) # Multiply your number by the power of the base that the digit represents
(1x16^3) + (15x16^2) + (2x16^1) + (0x16^0) # Convert the hex numbers into the decimal equivilent
4096 + 3840 + 32 + 0 = 7968 # Add the numbers together to get the result in BASE 10
Further Reading:
http://whatis.techtarget.com/definition/logic-gate-AND-OR-XOR-NOT-NAND-NOR-and-XNOR
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